Is there a way to create a seamless image in the compositor?
The question depends on the nature of the source image. In the Fireworks example the edge is already seamless (black). So you can use the compositor. Otherwise you would prepare the edges as the other answer suggests with a blending mask.


Import image
Add a Translate node, turn on "Wrap Both Axes"
Alter X and Y offset
You can add the original image back over the top with an "Add" mix
node.